In the figure, a uniform beam of mass M = 60.0 kg and length L = 5.0 m is suppor
ID: 1481364 • Letter: I
Question
In the figure, a uniform beam of mass M = 60.0 kg and length L = 5.0 m is supported in a horizontal position by a hinge and a cable, with angle theta = 70.0 degree. In addition there is a box ot mass m = 40.0 kg at the other end of the beam, as shown. Draw a free body diagram for the beam. Label all the forces, and draw distances relevant to the torques. Find the magnitude of the tension in the cable. Find the x-component (horizontal) of the force on the beam from the hinge. Find the y-component (vertical)of the force on the beam from the hinge.Explanation / Answer
form moment balance at hine point
(60*5/2 )*9.81 + 40*5*9.81 - (Tsin70)*5
T= 730.53N
from force balance in vertical 730.53-40*9.81-60*9.81+y component of hinge force=0
y component of hinge force = 250.46 N (positive means in upward direction)
from horizontal force balance
x component of hinge force + Tcos70 =0
x component of hinge force = -249.84N (negative means towards left)
when string is suddenly cut down than from torque= moment of inertia * angular acc
40*9.81*5+60*9.81*2.5 = (60*52 / 3) * angular acc
angular acc = 6.867 rad / s2